The height of a solid cylinder is 30 cm and the diameter of its base is 10 cm. Two identical conical holes each of radius 5 cm and height 12 cm are drilled out. What is the surface area (in cm²) of the remaining solid?

In ∆ABC, the bisector of ∠A intersects side BC at D. If AB = 12 cm, AC = 15 cm and BC= 18 cm, then the length of BD is:

The sum of the present ages of a father and son is 52 years. Four years hence, the son's age will be that of the father. What will be the ratio of the ages of the son and father, 10 years from now?

A can do a piece of work in 15 days. B is 25% more efficient than A, and C is 40% more efficient than B. A and C work together for 3 days and then C leaves. A and B together will complete the work in:

A and B are solutions of acid and water. The ratio of water and acid in A and B are 4 : 5 and 1 : 2, respectively. If x literes of A is mixed with y litres of B, then the ratio of water and acid in the mixture becomes 8 : 13. What is x : y ?

In ∆ABC, ∠A=90⁰ , AD is the bisector of ∠A meeting BC at D, and DE ⊥ AC at E. if AB = 10 cm and AC = 15 cm, then the length of DE, in cm, is:

if , then the value of (8x+5) is

The product of 1.7 ´ 10⁴ and 12.5 ´ 10^–6 is expressed in the standard form as k ´ 10ⁿ . The value of (2k + n) is